Lithium ion battery stacked porous electrode model construction method based on Dalaunay triangulation method and fractal modeling

Abstract

The invention relates to the technical field of lithium ion battery electrode modeling, and discloses a lithium ion battery stacked porous electrode model construction method based on a Dalaunay triangulation method and fractal modeling. According to the method, by designing a disordered particle generation function, the particle size has disordered random changes in x, y and z directions in a radial and axial three-dimensional Cartesian space coordinate system at the same time, randomly-agglomerated discrete particles take the circle center as a node to generate a conductive network, the generated triangular network has the property of minimum angle and maximum, and the particle size of the conductive network is smaller than that of the conductive network. According to the design, the micro-structure unit of the battery is adjusted in a manner of setting the same dispersity according to the change of the standard deviation and the particle size; and importing the established novel porous electrode structure into comsol simulation software to carry out lithium ion battery performance and mass transfer tests, exploring an influence rule of each particle microstructure on a lithium ion concentration field, local current density and overpotential distribution, and calculating corresponding battery energy density and power density.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of lithium ion battery electrode modeling, in particular to a lithium ion battery stacked porous electrode model construction method based on Dalaunay triangulation method and fractal modeling. BACKGROUND

[0002] With the transformation of global energy structure to clean and low carbon, as the core energy storage device in the field of new energy vehicles, smart grid and other fields, the performance optimization of lithium ion battery has become the key to promote the green energy revolution. However, the traditional lithium ion battery electrode design mainly relies on the experience and trial method, and the performance optimization is realized by adjusting the material composition or process parameters, which has the limitations of long cycle, high cost and difficulty in establishing the quantitative correlation between microstructure and macroscopic electrochemical performance. Although the existing model (such as pseudo two-dimensional model or homogeneous three-dimensional model) can partially reflect the electrode behavior, it ignores the micro-heterogeneity of the real electrode (such as random distribution of particles, poor connectivity of pores and fractal characteristics), which leads to insufficient prediction accuracy and cannot effectively guide the directional design of high energy density and high power density electrode. Specifically: It is difficult to model the three-dimensional heterogeneous structure: the traditional Delaunay triangulation algorithm is mainly used for two-dimensional plane or regular three-dimensional structure, while the active particles in lithium battery electrode are three-dimensional and randomly stacked, and the particle size distribution has gradient change (such as radial / axial dispersion), which makes it difficult for the traditional algorithm to directly represent the random spatial correlation between particles, and modeling distortion is easy to occur; Optimization contradiction of conductive network generation: the conductive agent in the electrode needs to form a continuous network between particles, but the triangular network generated by the traditional Delaunay algorithm is easy to produce "slim bridge structure" in three-dimensional space due to the particle agglomeration effect, resulting in uneven impedance of electron transport path; at the same time, if only the uniformity of the network is pursued, the balance of the porosity and ion transport channel of the electrode will be destroyed; Bottleneck of multi-physical field coupling calculation: when the conductive network generated by Delaunay triangulation is imported into the simulation software, due to the geometric complexity of three-dimensional structure (such as sharp angle, cross connection), it is easy to cause the decline of grid division quality, resulting in convergence problem when COMSOL and other software are calculated, which is difficult to accurately simulate the lithium ion concentration field and overpotential distribution; Lack of correlation between micro-parameters and performance: the existing research lacks systematic analysis on the synergistic mechanism of key parameters such as active particle size and discharge rate and battery energy / power density, and it is difficult to quantitatively reveal the influence of microstructure on dynamic behavior such as concentration polarization and potential distribution. SUMMARY

[0003] In view of the deficiencies of the prior art, the present application provides a lithium ion battery stacked porous electrode model construction method based on a Dalaunay triangulation method and fractal modeling, which has the advantages of solving the problems of three-dimensional modeling distortion, conductive network topology defects, and multi-physical field calculation bottlenecks of traditional algorithms in the application of lithium battery electrodes, realizing the collaborative optimization of electron / ion transmission paths, and improving the battery energy density and power density, thereby solving the above technical problems.

[0004] To achieve the above object, the present application provides the following technical scheme: a lithium ion battery stacked porous electrode model construction method based on a Dalaunay triangulation method and fractal modeling, comprising the following steps: S1: constructing a fractal stacked electrode model, creating a spherical particle size through a MATLAB program setting For 3.8 μm, standard deviation For 0.35, porosity For 0.35 random particle model, the particle distribution is constrained by the fractal dimension D f =2.75, and the generated model is imported into COMSOL software to generate a simple heterogeneous model by using COMSOL Multiphysics 6.1 with MATLAB instructions; S2: generating a conductive network for the random particle model in S1 by a Delaunay triangulation method, and generating a conductive agent structure between random particles by using a geometry generation module in COMSOL software; S3: setting the electrode, separator, particle and conductive agent of the battery structure in COMSOL software, and classifying the boundary of the entity surface and setting the material; S4: selecting the transient state of lithium ion battery with initialization, and inputting the battery discharge study; S5: calculating the discharge curve, and comparing the discharge curves at different discharge rates under the same particle size.

[0005] As a preferred technical scheme of the present application, the generation of the conductive network by the Delaunay triangulation method in S2 comprises: calculating the fractal correlation degree of the particle center, screening out the pivotal particles, and generating a conductive network for the pivotal particles.

[0006] As a preferred technical scheme of the present application, the fractal correlation degree has the following specific expression: Wherein, P i represents the i-th particle, d ij is the particle P i and Pj The distance between the center of the circle, r max is the maximum characteristic distance of the particle distribution in the system, M For P i Distance less than r max The total number of particles, Indicates summation.

[0007] As a preferred technical solution of the present invention, in S2, generating a conductive agent structure between random particles using the geometry generation module in COMSOL software includes: In the Delaunay triangulation process, the porosity-tortuosity coupling constraint is added, which is specifically expressed as: in, r max,s , r min,s represent the maximum and minimum radius of active particles, respectively. D f represents the area fractal dimension of porous media, L t ( λ ) the length of a single pipe, L 0 represents the characteristic length of the channel in the flow direction, τ Indicates the tortuosity, Indicates porosity.

[0008] Compared with the prior art, the present invention provides a method for constructing a lithium-ion battery stacked porous electrode model based on the Dalaunay triangulation method and fractal modeling, which has the following beneficial effects: The porous electrode structure designed and generated by the present invention takes into account the actual structure of the conductive agent in the battery. The design of the three-dimensional structure enables the porous electrode to have different density distributions along different directions, and is more in line with the battery structure characteristics than traditional homogeneous and one-dimensional electrode designs. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 The three-dimensional microstructure geometric model of the heterogeneous stacked porous electrode of the present invention constitutes a network framework geometric structure diagram; Figure 2 This is a schematic diagram of the grid division of the lithium-ion battery of the present invention; Figure 3 This is a comparison chart of the discharge curve of a lithium-ion battery at room temperature under 1C simulated by the stacking model of the present invention and the discharge experimental value under the same conditions; Figure 4 The discharge curves of the 3.8 μm electrode structure of the present invention at different discharge rates; Figure 5 Figure 1 is a diagram showing the distribution of lithium ion concentration along the thickness of the electrode at different magnifications according to the present application; Figure 6 Figure 2 is a diagram showing the energy density and power density of the electrode at three different particle sizes according to the present application; Figure 7 Figure 3 is a diagram showing the distribution of lithium ion concentration in the electrolyte and solid lithium ion concentration in the particle at different discharge magnifications at the same particle size according to the present application; Figure 8 Figure 4 is a diagram showing the discharge curves of three lithium ion batteries with particle sizes of 3.8, 4.8 and 5.8 μm obtained by simulation calculation according to the present application; Figure 9 Figure 5 is a diagram showing the Ragone diagram of three lithium ion batteries with particle sizes of 3.8, 4.8 and 5.8 μm obtained by simulation calculation according to the present application; Figure 10 Figure 6 is a diagram showing the change of lithium ion concentration in the electrolyte and lithium ion concentration in the particle with time at different particle sizes according to the present application; Figure 11 Figure 7 is a diagram showing the distribution of electrolyte potential at the cross section of the electrode active particle with an average particle size of 3.8 μm and 5.8 μm according to the present application; Figure 12 Figure 8 is a diagram showing the distribution of particle edge overpotential near the current collector at an average particle size of 3.8 μm and 5.8 μm according to the present application; Figure 13 Figure 9 is a diagram showing the distribution of surface overpotential of the electrode active particle at an average particle size of 3.8 μm and 5.8 μm according to the present application. DETAILED DESCRIPTION

[0010] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of the present application.

[0011] Please refer to Figures 1-13 , which comprises the following steps: (1) The construction of the fractal stacked electrode model, in which the parameter settings are created by a MATLAB program to set the spherical particle size (Rp) to 3.8 μm, the standard deviation (s) to 0.35, and the porosity (ε) to 0.35. The particle distribution is constrained by the fractal dimension Df = 2.75, so that the Delaunay subdivision nodes meet the radial particle size gradient variation (the traditional algorithm does not set this constraint), and are limited within a cuboid with a length, width, and height of 30 μm. The generated model is imported into the COMSOL software using COMSOL Multiphysics 6.1 with MATLAB instructions to generate a simple heterogeneous model; In the fractal stacked porous electrode modeling process: Based on the Gaussian distribution and fractal scaling law, a three-dimensional disordered stacking structure of active particles is generated to represent the particle size dispersion and random spatial distribution of real electrodes; In the porous electrode, there is a fractal characteristic, and the total number of pores with a pore length equal to or greater than λ fits the fractal scaling relationship of equation (1); (1) wherein, N is the total number of pores with a pore length equal to or greater than λ ; and L represents the capillary length; λ max and λ represent the maximum pore diameter and the pore diameter; D f represents the area fractal dimension of the porous medium; In the porous electrode, the number of pores is very large, so it can be considered as a continuous and differentiable function through theoretical calculation and method. After differentiating equation (2), the corresponding result can be obtained; (2) Node screening based on fractal dimension: By calculating the fractal correlation degree of the particle center (such as equations 3-4), the "hub particles" that play a decisive role in the connectivity of the conductive network are screened out, and Delaunay subdivision is only applied to such particles, reducing the three-dimensional subdivision calculation amount by more than 40%; For any particle P i , its fractal correlation degree is: wherein, d ij is the center distance between particles P i and P j ; and r maxThe maximum characteristic distance of the particle distribution in the system; M The characteristic distance of the particle distribution in the system is P i The total number of particles with a distance less than r max ; this formula quantifies the particle P i The spatial correlation strength of a particle with surrounding particles, The greater the value, the tighter the spatial distribution of the particle is correlated with other particles; For each particle P i Calculate its distance d ij with other particles, substitute the fractal correlation degree formula, and calculate the mean value of the correlation degree of all particles and the standard deviation σ, set the screening threshold value to (k is an empirical coefficient, usually 1.0~1.5); particles that meet The threshold value are defined as "hub particles", which are characterized by: spatial position at the key connection point of the particle network; play a bridge role in the formation of conductive paths (such as connecting multiple isolated particle clusters); If the distribution of electrode active material particles follows fractal characteristics, the total surface area of the particles can be represented as: (3) In the formula, r s R represents the radius of the active particle; r max,s , r min,s Rmax and Rmin represent the maximum and minimum radii of the active particles, respectively; In a porous electrode, the relationship between the length of a single pipe L t ( λ ) and the pipe diameter λ follows the fractal scaling law, which can be represented as: (4) In the formula, L 0 represents the characteristic length of the flow direction channel; L t L represents the actual length of the lithium ion path; D t D represents the tortuosity fractal dimension, and the greater the value, the more tortuous the channel; For any triangular patch △ in three-dimensional space ABC , there is no other particle center node P inside the circumscribed sphere, and the mathematical expression is: Any node P(x p , y p , zp ), meet ((x p -x0) 2 + (y p -y0) 2 + (z p -z0) 2 >R 2 where (x0, y0, z0) is the circumscribed sphere center, R is the circumscribed sphere radius; Optimization of three-dimensional subdivision criteria: In the process of Delaunay triangulation, increase the porosity-tortuosity coupling constraint (such as formula 5-6), by dynamically adjusting the edge weight value of the triangular network, preferentially retain the bridging structure that can meet the "minimum angle maximum property" and "particle empty circumscribed circle porosity connectivity condition", avoid generating long and thin conductive agent bridges that hinder ion transmission (traditional algorithm does not consider this constraint); Tortuosity can describe the complexity of the fluid passing through the path, and the symbol is τ , usually greater than 1, and the tortuosity can be expressed as: (5) where D t is the fractal dimension of tortuosity; The relationship between the size of the active particles and the porosity is: (6) Adaptive bridging radius adjustment: According to the particle size and spacing, dynamically adjust the conductive agent bridging radius through formula (7), so that the cross-sectional area of the bridging structure and the particle surface area are in a fractal proportion relationship, which not only ensures the electron transmission efficiency, but also avoids the decrease of porosity caused by the bridging of the coarse; where, ε is the electrode porosity; The pore size λ of formula 5 is related to the particle size and substituted into formula 6 to eliminate the particle size to obtain the power law coupling relationship between the two; (7) In the formula, S v indicates the specific surface area; A s indicates the total surface area of the electrode particles; V is the volume of the electrode; Use Delaunay triangulation method to generate conductive network, optimize the uniformity of electron transmission path, and avoid intersection and slender structure defects; (2) Using the geometry generation module in COMSOL software, the conductive agent structure is generated around the original particles by algorithm, and the Delaunay partition parameters are improved: the cylinder radius is set to "adaptive value = 0.4 x particle radius + 0.2 μm", and the bridge structure is screened through the following code, the cylinder radius is set to 1.5 μm, and the height of the cylinder is related to the distance between the particles. In order to ensure finer meshing in the simulation process and avoid errors in the calculation process, remove the excess entity, use the intersection in the software to divide each entity, then use the combination to remove the excess entity inside the ball, and combine it with the ball to form a whole, and the rest of the ball and the conductive agent are generated in the same way. The schematic diagram of the finally generated porous electrode structure model is shown in Figure 1 ; It is worth noting that, in order to embody the disorder of the porous structure, the conductive agent network structure connects the particles in a bridging manner to form an electrode path; the Delaunay triangulation method is used to ensure that the conductive agent is uniformly distributed in the electrode, and a triangular network is formed by using randomly generated disordered particle centers as nodes; the intersection and slender triangle of the triangular network are avoided by using the empty circumscribed circle property and the minimum angle maximum property to ensure its uniformity; the calculation speed of the generated particles decreases with the increase of porosity, and the porosity of the particles is more appropriate at 0.35; The structural details of the porous electrode are not subjected to homogenization treatment in the model geometry, and such a model is called a heterogeneous model; combined with the mass conservation and charge equation (equations 8-11), electrochemical kinetics equation (equations 12-16) and electrochemical reaction kinetics equation (equations 17-20), a three-dimensional heterogeneous microstructure model is established, and the calculation bottleneck is solved by the following method; Geometric preprocessing algorithm: "sharp angle smoothing treatment" is performed on the conductive network generated by Delaunay partition to improve the meshing quality to an average unit quality of 0.8 or more (the structure generated by traditional algorithm easily leads to a meshing quality of less than 0.5, causing calculation error); Regional solution strategy: the electrode domain is divided into "particle region" and "conductive agent region", high-resolution grid (cell size ≤0.1 μm) is used for particle core region, and adaptive grid encryption is used for bridging region, so that the convergence speed of COMSOL simulation is improved by 3 times (traditional algorithm uses uniform grid, which has low calculation efficiency); Mass conservation and charge equation The active particle control equation includes mass conservation and charge conservation. In the solid phase, the active particle is assumed to be a sphere, and the mass conservation of lithium ion is described by Fick's law; (8) In the formula, c1 represents the solid-phase lithium ion concentration in the battery electrode; D 1 represents the diffusion coefficient of the solid-phase active particle;t For time, the lithium concentration on the surface of the active particle and the transport concentration of lithium ions in the electrolyte solution are coupled with the flux, and the lithium ion flux in the particle is zero; The solid phase charge conservation is described by Ohm's law; (9) In the formula, Φ s The solid phase electrode potential is represented by, σ eff The solid phase electrode effective conductivity is represented by, S v The specific surface area is represented by, In the liquid phase electrolyte area, the change of lithium ion concentration in the electrolyte solution is described, the migration and diffusion of lithium ions in the process, and the mass conservation in the liquid phase is represented by the following equation: (10) In the formula, c2 represents the lithium ion concentration in the electrolyte liquid phase, v + The amount of lithium ion generated per mole of electrolyte dissociation is represented by, i 2 represents the electrolyte liquid phase current density, t + The lithium ion electromigration number is represented by, and the right side respectively represents the diffusion term, the migration term and the reaction term, which describes the diffusion of lithium ions due to concentration, the migration along the electric field direction in response to the electric field, and the reaction controlled by the electrode surface and the electrolyte interface; Liquid phase charge conservation (11) In the formula, Φ e The liquid phase electrode potential is represented by, κ eff The liquid phase ion conductivity is represented by; Electrochemical kinetics equation: The total reaction equation of ternary lithium battery is shown in the formula; The positive electrode reaction is: (12) The mass conservation and the material conservation control variable are explained by Butler-Volmer, which constitutes the electrochemical kinetics equation; (13) In the formula, i 0 represents the exchange current density, α a The negative electrode transfer coefficient is represented by, α c The positive electrode transfer coefficient is represented by, R is a general gas constant,η s overpotential, F F is the Faraday constant, and the overpotential is defined as (14) where, U U0 is the equilibrium potential of the electrode, which is related to temperature and state of charge, and is expanded to the first order by Taylor's formula as (15) where, U ref U0 is the equilibrium potential of the electrode, which is related to temperature and state of charge, and is expanded to the first order by Taylor's formula as T ref T is the reference temperature; (16) where, cmax 1,max cmax is the maximum concentration of lithium ions in the electrode material, and c 1,surf c is the surface concentration of lithium ions Energy conservation equation The temperature change of the battery follows the energy conservation equation: (17) The heat sources generated by the battery mainly include three parts: polarization heat, reaction heat, and ohmic heat. (18) (19) (20) where, ρ is the density of the battery, C p is the heat capacity of the battery, Q is the average internal heat generation, Q rev , Q rea and Q ohm represent the polarization heat, reaction heat, and ohmic heat, respectively. The concentration fields of solid / liquid phases, potential distribution, and overpotential fluctuation are solved by finite element software (such as COMSOL), and the effects of discharge rate and particle size on energy / power density are analyzed. (3) In the COMSOL software, the electrodes, separators, particles, and conductive agents of the battery structure are set up with names, and the boundaries of the entity surfaces are classified, then the materials are set, and the positive electrode material is Li(NiCoMn) 1 / 3O2, lithium metal foil electrode, separator, electrolyte is a lithium ion battery electrolyte composed of lithium hexafluorophosphate (LiPF6) as lithium salt, ethylene carbonate (EC) and methyl ethyl carbonate (EMC) mixed in a volume ratio of 3:7. The model is based on software using lithium ion battery module and rare substance transfer module to solve, in order to simplify, the current collector is simplified as the boundary of the electrode domain through the current boundary condition. The electrolyte potential, electrolyte salt concentration and potential in lithium ion battery are discretized linearly, the electrode reaction in the internal electrode surface is set on the particle surface, the concentration interface input c is set, the lithium ion insertion is set in the electrode kinetics, the reference exchange current density is 10A / m 2 , the lithium foil electrode surface exchange current density is set to 100A / m 2 , the electrode current is set on the surface of the current collector, the discharge current and discharge rate are set to 1C, the inward electrode current is calculated, and the initial value of the boundary potential is set to 4.4V. The convection in the transfer mechanism is cancelled at the rare substance transfer interface, and the lithium surface intercalation flux is coupled to the electrochemical reaction at the particle surface electrode surface coupling node. The battery performance parameters are shown in Table 1, the domain element number is set to 6258226 by dividing the grid, the minimum element mass is 0.01312, and the average element mass is 0.6569. The grid quality is good, and the grid division is shown in Figure 2 , and finally the research calculation model is added; Table 1 (4) Find the research interface, select the lithium ion battery with initialization transient, enter the battery discharge research, under the step one current distribution initialization node, the electrode distribution type is selected twice. Then set the transient time in step 2, output time step (0 0.5 / C_rate 1.5 / C_rate 2.5 / C_rate) output 4 times related to the rate, set the stop condition under the solution 1 node to set the cutoff voltage to 3V, and stop the research when the voltage meets the condition. The electrolyte concentration dependent variable is placed in a separate group to reduce the memory requirement of the solution; (5) The discharge curve is obtained by calculation Figure 4 The discharge curves at different discharge rates under the same particle size are compared, which shows the relationship between voltage and time at four rates of 0.5C, 1C, 2C and 5C. At lower rates (0.5C and 1C), the energy loss is minimum, showing a relatively gentle downward trend; high rates (2C and 5C) can release energy faster, resulting in rapid voltage drop.

[0012] Set different particle sizes (3.8μm, 4.8μm, 5.8μm) and discharge rates (0.5C-5C) simulation conditions; Based on the Ragone graph and the concentration gradient distribution, the electrode performance is quantitatively evaluated, and the high specific energy and high power electrode design is guided. Compared with the traditional Delaunay triangulation algorithm, the improved scheme realizes the following breakthroughs: Modeling accuracy is improved: through fractal-gradient constraint, the error of the porosity simulation value of the three-dimensional electrode model and the experimental value is reduced to ±3.5%, which is closer to the real electrode structure.

[0013] Conductive network performance optimization: the contact resistance of the conductive agent bridging structure is reduced by 47%, the electron transport efficiency is improved by 32%, and the porosity retention rate is improved from 68% of the traditional algorithm to 89%, balancing electron conduction and ion diffusion.

[0014] Simulation efficiency is improved: through geometric preprocessing and regional solving, the COMSOL simulation time is shortened from 24 hours of the traditional method to 8 hours, and the convergence stability is improved, with a repeatability error of less than 2%; In order to more intuitively see the lithium ion concentration change of the whole electrode, a cross section line passing through the center of the electrode is drawn to extract the data on the cross section line Figure 5 , the abscissa is the cross section length size passing through the center of the electrode, and the ordinate is the solid-phase lithium ion concentration along the thickness direction of the electrode from the current collector to the separator. Due to the incomplete contact of the horizontal cross section with the particles, there is a small positional interval; there is a concentration difference between the surface and the center of a single particle, which is not obvious at low rate, and the concentration difference decreases by 27.66%, 12.77% and 6.38% from the surface to the center at 5C rate. The concentration difference will cause uneven stress distribution in the particle and change the diffusion of lithium ions. The stacked porous electrode structure with an average particle size of 3.8 μm is not suitable for use at high rate.

[0015] The particle size parameter in the lithium ion battery positive active particle is one of the important parameters affecting the battery performance. The energy density and power density of the electrode at different particle sizes of 3.8 μm, 4.8 μm and 5.8 μm are calculated, Figure 6 It can be seen from the above that at the same particle size, the energy density decreases significantly with the increase of the rate, and generally decreases to 60-65% of the low rate at 5C. The power density gradually increases with the increase of the rate, and reaches the peak value of 251-306% of the low rate at 5C. The increase slows down with the increase of the particle size. This is because at high rate, the lithium ion migration speed increases, but the lithium ion insertion and extraction reaction time in the electrode material shortens, resulting in incomplete reaction (such as insufficient utilization of active material), and the energy density decreases. The power density reflects the high-rate charge and discharge capacity of the battery. When the rate increases, the ion migration rate matches the current demand, the electrode polarization effect increases, and higher power density can be released, so the power density increases with the increase of the rate.

[0016] The distribution of lithium ion concentrations in the electrolyte and solid lithium ions in the particles at different discharge rates at the initial discharge stage of the electrode structure with the same particle size was calculated through simulation. In the positive electrode material particle area, the concentration of solid lithium (denoted as c1) is displayed, while in other areas, the concentration of lithium ions in the electrolyte (denoted as c2) is displayed. According to the discharge curve under 1C proposed in this article, the voltage time point after 10% discharge is completed is regarded as the initial discharge stage, and the time point when the voltage begins to drop sharply is regarded as the end of discharge.

[0017] Under low-rate conditions, the solid-state lithium ion concentration distribution within the particles is relatively uniform; as the rate increases, the concentration gradient within the particles gradually intensifies, and at high rates, the concentration difference in local areas is more obvious. This is because the electrochemical reaction rate is much higher than the solid-state diffusion rate of lithium ions within the electrode particles. The surface lithium ions are rapidly consumed, and internal diffusion is difficult to replenish in real time, resulting in a large gradient in the lithium ion concentration within the particles. Especially in the center of the battery particles, the lithium ion "concentration polarization" phenomenon is exacerbated due to the restricted diffusion of lithium ions. When the liquid-phase lithium ion concentration is at low rates, the lithium ion concentration distribution in the electrolyte is relatively balanced; at high rates, the liquid-phase concentration gradient increases significantly, the uniformity is gradually destroyed, and the concentration in the interface area decreases significantly. Because the consumption rate of lithium ions by the reaction is accelerated, the ion migration in the electrolyte cannot be compensated in time, resulting in a significant decrease in the concentration in the local area.

[0018] By controlling the particle size dispersion (average particle size / standard deviation) to be the same, these particles of different sizes are randomly stacked in the electrode. Figure 8 and Figure 9After modeling with the stacking model, the discharge curves and Ragone plots of three kinds of lithium-ion batteries with 3.8, 4.8 and 5.8 μm were obtained by simulation calculation. It can be seen from them that the voltage platform of small particle size is longer and smoother, and the discharge capacity is the largest, which shows that it can provide higher effective capacity, while the large particle size has significantly decreased performance due to diffusion limitation. From the overall trend, they all show a significant negative correlation trend, and the energy density gradually decreases as the power density increases from 500 W / L to 3000 W / L. From the difference of different particle sizes, the electrode with an average particle size of 3.8 μm has a significant advantage in energy density, and when the power density is 500 W / L, the energy density can reach about 1050 Wh / L, even if the power density increases to 2500 W / L, it still maintains an energy density of about 830 Wh / L, and finally stabilizes at 700 Wh / L at 3000 W / L; the energy density of the electrode with an average particle size of 4.8 μm has a moderate decay rate with the increase of power density, and the energy density is about 1030 Wh / L at 500 W / L, decreases to 800 Wh / L at 2000 W / L, and is about 680 Wh / L at 3000 W / L, the overall performance is between 3.8 μm and 5.8 μm; the energy density of the electrode with an average particle size of 4.8 μm decays most obviously. 500 W / L is about 1000 Wh / L, and when the power density increases to 2000 W / L, the energy density drops to 760 Wh / L, and further to less than 650 Wh / L at 3000 W / L. The main reason is that small particle size shortens the diffusion path of lithium ions, reduces the charge transfer impedance, and makes it still maintain a high energy output at high power density; large particle size leads to the extension of ion diffusion path, and the polarization effect is more significant, which seriously affects the energy retention ability at high power.

[0019] In order to more intuitively describe the geometric structure in the electrode, the transfer process of lithium ions in the liquid phase diffusion of porous electrode and the solid phase in the electrode material is presented as follows: Figure 10The concentration distribution of lithium ions in the electrolyte and in the solid state within the particles of the positive electrode active material with different average particle sizes is shown at the 5C discharge condition at the initial and final stages of discharge. When the average particle size is small, the concentration gradient of lithium ions in the particle is the smallest, and when the average particle size is large, the concentration gradient of lithium in the particle is the largest. For a single positive electrode particle, at the initial stage of discharge, the surface of the particle has a high concentration of solid-state lithium, and there is a significant concentration gradient in the radial direction of the particle. However, at the final stage of discharge, the concentration of solid-state lithium in the positive electrode material particle has little difference in the radial direction and tends to be uniform in the direction parallel to the current collector. By comparing the lithium concentration of particles of different sizes at the initial stage of discharge, it can be further found that the smaller the particle size, the smaller the concentration difference of solid-state lithium in the single particle; on the contrary, the larger the particle size, the more obvious the concentration difference of solid-state lithium in the single particle, which indicates that reducing the particle size helps to reduce the transport resistance of solid-state lithium in the particle; and the concentration of liquid-state lithium ions is relatively high on the surface of the particle with a large particle size, and is unevenly distributed, and lithium ions have not been completely inserted from the electrolyte into the electrode particles, especially in the area where the particle surface contacts the separator.

[0020] For the overall positive electrode, at the initial and final stages of discharge, there is a large range of concentration change regions in the internal solid-state lithium concentration distribution of the positive electrode with small particle sizes, which tends to be uniform in the direction parallel to the current collector, showing the mode of lithium ion diffusion throughout the electrode. Increasing the particle size increases the difficulty of the diffusion of solid-state lithium ions in the particle, and the concentration distribution of the internal solid-state lithium of the positive electrode presents a similar situation, i.e., the surface of the particle near the separator always has a higher concentration of solid-state lithium than the particle near the current collector. Notably, at the final stage of discharge, the amount of lithium insertion near the separator increases as the particle size decreases, which is consistent with the consensus of numerous studies; and the amount of lithium insertion in the positive electrode particle near the current collector decreases as the particle size decreases. That is, as the particle size decreases, the concentration difference of solid-state lithium at both ends of the positive electrode increases. For a larger active particle, lithium ions need to travel a long path to reach the center of the particle, so the large particle cannot be properly lithiated, and the uneven distribution of large particles also leads to a higher loss of energy density.

[0021] In order to more intuitively observe the influence of particle size on the micro performance of the battery, the distribution diagrams of electrolyte potential, local current density and overpotential of particles with small and large particle sizes of 3.8 μm and 5.8 μm are extracted, Figure 11 The cross-sectional diagram of the electrolyte potential distribution of the electrode active particles with average particle sizes of 3.8 μm and 5.8 μm is shown in FIG. 8. From the diagram, it can be seen that the potential of the electrolyte in the positive electrode is not uniform, and the potential of the electrolyte in the positive electrode is not uniform. Figure 11 (a) and Figure 11(b) It can be clearly seen that the electrolyte potential varies from high to low from lithium metal to the current collector in the whole electrode reaction area, but the performance shows differences under different average particle sizes. The electrolyte potential changes more gently and uniformly for smaller particles, mainly concentrated around the particles. The potential of the electrolyte changes greatly near the particles, but the potential remains almost the same in the area far from the particles. However, the potential changes significantly for larger particles, especially in the area around the particles. Here, the potential gradient is large, which may indicate that the ion flow of the electrolyte is hindered to a certain extent in the case of larger particles, resulting in uneven potential. The main reason is that the particle size directly affects the potential distribution of the electrolyte. Smaller particles can provide more surface area, which is conducive to the uniform distribution of the electrolyte and ion diffusion; while larger particles reduce the surface area, limiting the conduction of electrolyte ions on the particle surface, resulting in a larger potential gradient. As the particle size increases, the potential distribution inside the battery may become more uneven, thereby affecting the performance of the battery, especially in the ion migration and reaction rate of the electrolyte.

[0022] Figure 12 The local current density and overpotential distribution near the current collector for particles with average particle sizes of 3.8 pm and 5.8 pm are compared. From Figure 12 (a) and Figure 12 (b) It can be seen from the comparison that the local current density and overpotential near the current collector present an inverted U-shaped distribution under an average particle size of 5.8 pm, i.e. the local current density and overpotential are higher in the area far from the separator on the surface of larger particles, and the maximum fluctuation range is about 80.01 and 65.96%. Under an average particle size of 3.8 pm, the fluctuation of both distributions is smaller and lower than that on the surface of larger particles, and the maximum fluctuation range is about 14.01% and 13.88%. The main reason is that the active particles near the current collector are more directly in contact with the current collector, the electron migration path is shorter, the resistance is lower, resulting in higher local current density. The specific surface area of smaller particles is larger. Under the condition of fixed total current, the large surface area will lead to a decrease in the amount of current per unit area, the local current density is higher, and the overpotential required for charge transfer is larger, resulting in enhanced electrochemical polarization; on the contrary, the local current density and overpotential of larger particles are higher, and the large particles have a long diffusion path, resulting in significant concentration polarization, which requires a higher driving force to maintain, further increasing the local current density.

[0023] Figure 13 The overpotential distribution diagrams of the positive active particle surfaces of two different average particle sizes (3.8 pm and 5.8 pm) are shown in Figure 13 (a) and Figure 13(b) It can be seen from the comparison in (b) that the overpotential near the separator is higher than that near the current collector at different particle sizes. This is mainly because the active particles near the current collector are in more direct contact with the current collector, the electron migration path is shorter, the resistance is lower, and the local current density is concentrated, resulting in higher overpotential. In the case of reducing the particle size, the overpotential value of the particle surface increases. This is because the current density of smaller particles is more uniform, the internal and external resistance of the battery is smaller, which is consistent with the overpotential distribution generated during the discharge process; the internal resistance of large particles is large, and the migration speed of lithium ions in the particles is slow, resulting in a significant difference in current density inside and outside the particles, thereby generating different overpotential values on the surface.

[0024] In summary, the regulation of discharge rate on battery performance, at high discharge rate (5C), the diffusion rate of lithium ions in the solid phase particle interior significantly lags behind the surface reaction rate, triggering concentration polarization effect, resulting in energy density decrease about 35-40% compared with 0.5C, voltage platform shortens and falls rapidly. The power density increases significantly with the increase of rate, which can reach 251-306% of low rate at 5C, but the local lithium ion concentration gradient of electrolyte is intensified at high rate, and the interface reaction inhomogeneity is enhanced, which limits the energy density retention ability. The synergistic effect of particle size on diffusion dynamics and energy / power density, reducing the average particle size of active particles (such as 3.8 μm) can shorten the solid-phase diffusion path of lithium ions, reduce the concentration gradient inside the particle (27.66% lower than 5.8 μm particles), and significantly improve the energy density (1050 Wh / L at 500 W / L) and high-rate performance. Large particle size particles (such as 5.8 μm) have a longer diffusion path, resulting in more severe concentration polarization, and the energy density decreases more significantly with the increase of power density (decreased to below 650 Wh / L at 3000 W / L), but due to its small volume change, the electrode structure is more stable. The regulation mechanism of microstructure on potential and overpotential distribution, small particle size particles optimize the uniformity of electrolyte potential distribution by increasing the specific surface area, and the fluctuation range of local current density is reduced to 14.01%, and the overpotential distribution is more balanced; while large particle size particles have a large diffusion resistance, and the fluctuation of surface overpotential is as high as 65.96%, which aggravates the electrochemical polarization. The particles near the separator have a complex lithium ion transport path, and the overpotential is generally higher than that on the current collector side, and the overpotential distribution of small particle size particles is more uniform; Set different particle sizes (3.8 μm, 4.8 μm, 5.8 μm) and discharge rates (0.5C-5C) simulation conditions; Based on the Ragone chart and concentration gradient distribution, the electrode performance is quantitatively evaluated to guide the design of high specific energy and high power electrodes. Compared with the traditional Delaunay triangulation algorithm, the improved scheme of the present application realizes the following breakthroughs: Modeling accuracy improvement: By fractal-gradient constraint, the error between simulated and experimental porosity of 3D electrode model is reduced to ±3.5%, which is closer to the real electrode structure.

[0025] Conductive network performance optimization: The contact resistance of conductive agent bridging structure is reduced by 47%, the electron transport efficiency is improved by 32%, and the porosity retention rate is improved from 68% of traditional algorithm to 89%, which balances electron conduction and ion diffusion.

[0026] Simulation efficiency improvement: Through geometric preprocessing and regional solving, the COMSOL simulation time is shortened from 24 hours of traditional method to 8 hours, and the convergence stability is improved, and the repeatability error is <2%; Although embodiments of the present application have been shown and described, it is to be understood that various modifications, substitutions, replacements and changes can be made to these embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for constructing a lithium-ion battery stacked porous electrode model based on the Dalaunay triangulation method and fractal modeling, characterized by: The following steps are involved: S1: Construct a fractal stacked electrode model and create spherical particle size through MATLAB program settings 3.8μm, standard deviation 0.35, porosity For the 0.35 random particle model, the fractal dimension D f = 2.75 constrained particle distribution, confined to the interior of a cuboid with a length, width, and height of 30 μm, and the generated model was imported into the simple heterogeneous model generated in COMSOL software using COMSOL Multiphysics 6.1 with MATLAB command; S2: Generate a conductive network for the random particle model in S1 using the Delaunay triangulation method, and use the geometry generation module in COMSOL software to generate a conductive agent structure between the random particles; S3: Name the electrodes, separators, particles, and conductive agents of the battery structure in COMSOL software, and classify the boundaries of the solid surface and then set the materials; S4: Select Li-ion battery transient with initialization and type battery discharge study; S5: Calculate the discharge curve and compare the discharge curves at different discharge rates under the same average particle size.

2. The method for constructing a lithium-ion battery stacked porous electrode model based on the Dalaunay triangulation method and fractal modeling according to claim 1, characterized in that: The generating of the conductive network by the Delaunay triangulation method in S2 includes: screening out hub particles by calculating the fractal correlation degree of the centers of particles, and generating a conductive network for the hub particles.

3. The method for constructing a lithium-ion battery stacked porous electrode model based on the Dalaunay triangulation method and fractal modeling according to claim 2, characterized in that: The specific expression of the fractal correlation is as follows: in, P i represents the i-th particle, d ij For particles P i and P j The distance between the center of the circle, r max is the maximum characteristic distance of the particle distribution in the system, M For P i Distance less than r max The total number of particles, Indicates summation.

4. The method for constructing a lithium-ion battery stacked porous electrode model based on the Dalaunay triangulation method and fractal modeling according to claim 3, characterized in that: In S2, the conductive agent structure is generated between random particles using the geometry generation module in COMSOL software, including: In the Delaunay triangulation process, the porosity-tortuosity coupling constraint is added, which is specifically expressed as: in, r max,s , r min,s represent the maximum and minimum radius of active particles, respectively. D f represents the area fractal dimension of porous media, L t ( λ ) represents the length of a single pipe, L 0 represents the characteristic length of the channel in the flow direction, τ Indicates the tortuosity, Indicates porosity.

Images